Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class HelloWorld
{    public static void main(String []args)throws IOException
     {  int i,j;
        long z=(long)Math.pow(10,9)+7;
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out=new PrintWriter(System.out);
        int n=Integer.parseInt(br.readLine());
        int m=0;
        if(n>=2)
        {   if(n%2==1)
                m=(n+1)/2;
            else
                m=(n+2)/2;
            int a[][]=new int[m][m];
            int temp=0,counter=1;
            for(i=0;i<m;i++)
            {   if(temp<m)
                    a[i][temp]=counter++;
                else
                    break;
                if(temp+1<m)
                    a[i][temp+1]=counter++;
                temp++;
            }
            out.println(m);
            for(i=0;i<m;i++)
            {   for(j=0;j<m;j++)
                  { if(a[i][j]>0 && a[i][j]<=n)
                        out.println((i+1)+" "+(j+1));
                  }    
            }
        }
        else
        {   out.println(1);
            out.print("1 1");
        }
        
        out.close();
         
     }
     
}